设函数f(x)在(0,1]内连续可导,且lim(x趋向于0+)(√x)f`(x)存在,证明f(x)在(0,1]内一致连续
我知道要把问题归结到证明lim(x趋向于0+)f(x)存在,如何由lim(x趋向于0+)(√x)f`(x)存在导出lim(x趋向于0+)f(x)存在,高手指点
人气:496 ℃ 时间:2019-08-17 13:42:33
解答
个人认为没必要先证limf(x)存在,将其作为一致连续性的推论更合适(用Cauchy收敛准则).f'(x)在(0,1]连续,lim(√x)f'(x)存在,可得(√x)f'(x)在(0,1]有界,设有|(√x)f'(x)| < M.对任意a,b∈(0,1],a < b,在[a,b]上对f(x)...
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